Derivatives · Pro · 4 min

The Greeks: delta, gamma, theta, vega

You can explain what delta, gamma, theta and vega measure and use them to estimate how an option's price reacts to price, time and volatility.

An options dashboard

A share's price depends mainly on one thing: what buyers and sellers pay for it. An option's price reacts to several things at once: the underlying's price, the time left and how much the market expects prices to swing.

Professionals describe these reactions with a set of measures named after Greek letters. They sound academic, but they work like a car's dashboard. This lesson explains the four you will see most often.

Price, time, volatility

The Options Industry Council, the education arm of the US options clearing house, defines them:

Delta measures how much an option's price changes when the underlying moves by one unit. At-the-money options have a delta of about 0.50, deep in-the-money calls approach 1.00. Puts have negative delta.
Gamma measures how fast delta itself changes when the underlying moves. Gamma is highest for at-the-money options and grows as expiry approaches.
Theta measures the change in an option's value for a one-day reduction in time to expiry. For option buyers, theta is usually negative: they lose value every day.
Vega measures the change in an option's value for a one-point change in volatility. Buyers of options gain when expected volatility rises, so vega is positive for them.

There are more Greeks, such as rho for interest rates, but these four cover the main risks.

The Greeks are estimates for small changes, and they change themselves as the market moves. The OIC recommends looking at them together, not in isolation. A position can gain on delta and lose on theta and vega at the same time.

+1.00 −0.05 −0.30

A fictional call option costs 4.00. Its Greeks: delta 0.50, theta −0.05, vega 0.10.

Over one day:

the underlying rises 2: delta effect ≈ 0.50 × 2 = +1.00,
one day passes: theta effect ≈ −0.05,
expected volatility falls by 3 points: vega effect ≈ 0.10 × −3 = −0.30.

Estimated new price: about 4.00 + 1.00 − 0.05 − 0.30 = 4.65. The trader was right about the direction, but the fall in volatility took away almost a third of the gain.

Common mistakes

Watching only delta. Time and volatility can outweigh a correct direction.
Treating Greeks as constants. They change with every move.
Ignoring gamma near expiry. Positions can flip from small to large exposure fast.
Selling options without measuring vega. A jump in volatility can hurt badly.

The takeaway

Delta shows sensitivity to the underlying's price, gamma how fast delta changes, theta the daily time decay and vega sensitivity to volatility.

Check yourself

Quick quiz

4 questions. Instant feedback, nothing is saved.

1Tap the Greek that tells you how much value an option loses per day.

Tap the chart.

The OIC defines theta as the change in option value for a one-day reduction in time until expiration.
2A call has a delta of 0.50. The underlying rises 2. How much does the call's price change, roughly?

Delta × price change = 0.50 × 2 ≈ 1, per share.
3What does vega measure?

Higher expected volatility makes options more valuable, so long options have positive vega.
4Where is gamma usually highest?

Near expiry, an at-the-money option's delta can swing quickly between near 0 and near 1.

of 4 correct.